Hints of unitarity at large N in the O(N )3 tensor field theory

Benedetti, Dario; Gurău, Razvan; Harribey, Sabine; Suzuki, Kenta

doi:10.1007/jhep02(2020)072

Cited by 26 publications

(58 citation statements)

References 117 publications

(197 reference statements)

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“…[8,11], or ζ = d/4, as in Ref. [16,17]). I d , I p and I t are the double-trace, pillow, and tetrahedron interactions, respectively:…”

Section: Spontaneous Symmetry Breaking At the Classical Levelmentioning

confidence: 99%

“…On the contrary, the invariant I t has indefinite sign and is unbounded, therefore the sign of its coupling cannot be fixed by stability requirements. In fact it could even be taken purely imaginary [16,17], similarly to the ϕ 3 interaction in the Lee-Yang model [28,29]. In this paper we will mostly assume λ t ∈ R, because we are interested in real solutions of the equations of motion, and we will assume that the theory makes sense in the large-N limit.…”

Section: Spontaneous Symmetry Breaking At the Classical Levelmentioning

confidence: 99%

“…and g ∈ SO (3). Notice that the properties (92) and (90) of the Wigner D-matrices imply that R m 1 m 2 satisfies the reality condition (17) and the orthogonality relation (19). Hence equations (14) and (35) define an N -dimensional orthogonal representation of SO(3).…”

Section: So(3)-invariant Solutionmentioning

confidence: 99%

“…For d = 1, with Grassmann rather than bosonic fields, they provide an alternative to the SYK model, without the need of quenched disorder [7][8][9][10]. Lastly, for d ≥ 2, they represent a novel class of quantum field theories for which we can hope to control nonperturbative aspects via the large-N limit, and in particular discover new interacting conformal field theories [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…The latter, in turn, is typically characterized by a universal critical behavior associated to the properties of a renormalization group fixed point lying on the boundary between two or more phases. As new classes of fixed points are being identified in tensor models in d ≥ 1 [11][12][13][14][15][16][17], it is natural to ask if they are associated to a phase transition, and in case of what kind. Understanding SSB in tensor models is a first step in order to address that.…”

Section: Introductionmentioning

confidence: 99%

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SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
Self Cite
14
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11
0
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We study classical and quantum (at large-N ) field equations of bosonic tensor models with quartic interactions and O(N ) 3 symmetry. Among various possible patterns of spontaneous symmetry breaking we highlight an SO(3) invariant solution, with the tensor field expressed in terms of the Wigner 3jm symbol. We argue that such solution has a special role in the large-N limit, as in particular its scaling in N can provide an on-shell justification for the melonic large-N limit of the two-particle irreducible effective action in a broken phase.

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“…[8,11], or ζ = d/4, as in Ref. [16,17]). I d , I p and I t are the double-trace, pillow, and tetrahedron interactions, respectively:…”

Section: Spontaneous Symmetry Breaking At the Classical Levelmentioning

confidence: 99%

Section: Spontaneous Symmetry Breaking At the Classical Levelmentioning

confidence: 99%

Section: So(3)-invariant Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
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14
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11
0
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Finite-size versus finite-temperature effects in the critical long-range O(N) model

Benedetti,

Gurau,

Harribey

et al. 2024

J. High Energ. Phys.

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In this paper we consider classical and quantum versions of the critical long-range O(N) model, for which we study finite-size and finite-temperature effects, respectively, at large N. First, we consider the classical (isotropic) model, which is conformally invariant at criticality, and we introduce one compact spatial direction. We show that the finite size dynamically induces an effective mass and we compute the one-point functions for bilinear primary operators with arbitrary spin and twist. Second, we study the quantum model, mapped to a Euclidean anisotropic field theory, local in Euclidean time and long-range in space, which we dub fractional Lifshitz field theory. We show that this model admits a fixed point at zero temperature, where it displays anisotropic Lifshitz scaling, and show that at finite temperature a thermal mass is induced. We then compute the one-point functions for an infinite family of bilinear scaling operators.In both the classical and quantum model, we find that, as previously noted for the short-range O(N) model in [1], the large-N two-point function contains information about the one-point functions, not only of the bilinear operators, but also of operators that appear in the operator product expansion of two fundamental fields only at subleading order in 1/N, namely powers of the Hubbard-Stratonovich intermediate field.

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Remarks on a melonic field theory with cubic interaction

Benedetti

Delporte

2021

J. High Energ. Phys.

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We revisit the Amit-Roginsky (AR) model in the light of recent studies on Sachdev-Ye-Kitaev (SYK) and tensor models, with which it shares some important features. It is a model of N scalar fields transforming in an N-dimensional irreducible representation of SO(3). The most relevant (in renormalization group sense) invariant interaction is cubic in the fields and mediated by a Wigner 3jm symbol. The latter can be viewed as a particular rank-3 tensor coupling, thus highlighting the similarity to the SYK model, in which the tensor coupling is however random and of even rank. As in the SYK and tensor models, in the large-N limit the perturbative expansion is dominated by melonic diagrams. The lack of randomness, and the rapidly growing number of invariants that can be built with n fields, makes the AR model somewhat closer to tensor models. We review the results from the old work of Amit and Roginsky with the hindsight of recent developments, correcting and completing some of their statements, in particular concerning the spectrum of the operator product expansion of two fundamental fields. For 5.74 < d < 6 the fixed-point theory defines a real CFT, while for smaller d complex dimensions appear, after a merging of the lowest dimension with its shadow. We also introduce and study a long-range version of the model, for which the cubic interaction is exactly marginal at large N , and we find a real and unitary CFT for any d < 6, both for real and imaginary coupling constant, up to some critical coupling.

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Hints of unitarity at large N in the O(N )3 tensor field theory

Cited by 26 publications

References 117 publications

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
Self Cite
14
0
11
0
View full text Add to dashboard Cite

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
Self Cite
14
0
11
0
View full text Add to dashboard Cite

Finite-size versus finite-temperature effects in the critical long-range O(N) model

Remarks on a melonic field theory with cubic interaction

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Hints of unitarity at large N in the O(N )3 tensor field theory

Cited by 26 publications

References 117 publications

SO(3) -invariant phase of the O(N)3Benedetti1, Costa2 2020Phys. Rev. DSelf Cite140110View full textAdd to dashboardCite

SO(3) -invariant phase of the O(N)3Benedetti1, Costa2 2020Phys. Rev. DSelf Cite140110View full textAdd to dashboardCite

Finite-size versus finite-temperature effects in the critical long-range O(N) model

Remarks on a melonic field theory with cubic interaction

Contact Info

Product

Resources

About

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
Self Cite
14
0
11
0
View full text Add to dashboard Cite

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
Self Cite
14
0
11
0
View full text Add to dashboard Cite